Arrow and Pratt [1]} found, that the more a utility function is concave, the higher the corresponding \(\textit {certainty equivalent}\)  is. This is the riskfree alternative outcome that would be considered to be equivalent to the expected utility of a fixed lottery by an investor. For the same risky situation, the more risk-averse an investor is, the smaller is his certainty equivalent. As a very extreme example think of a highly risk-averse person, that, even if negative riskfree interest rates would actually reduce his wealth, he still would prefer this option over the uncertainty of the outcome of a stock with attractive expected return. But for decreasing interest rates, at some point, even he might be willing to invest in the risky asset. This interest would then be considered to be the certainty equivalent to the stock. Since it can be shown that if one utility function is tranformed by a concave function then its certainty equivalent is decreasing, the link from risk aversion to the convexity of the utility function is established. This motivates the definition of the measure for risk aversion ((6) in [1]}), called the coefficient of absolute risk aversion:
